Name: ________________________ Date: ____________ Notes: Classifying Numbers Do Now: Match each description with the set of numbers that most appropriately be represents it. No repeating. 1 2 5 13 _____ Money A. { , , , … } 6 5 9 14 _____ Number of Students in Class B. {… , −2.50, 0.00, 5.25, 16.73, … } _____ Golf Score C. {… − 2, −1,0, +1, +2 … } _____ Fraction of a Whole D. {0,1,2,3,4,5,6,7, … } Using the diagram to the right, match each of the number sets with its name. ___ Real Number A. {1,2,3,4, … } ___ Irrational Numbers B. {0,1,2,3,4, … } ___ Rational Numbers C. {… , −2, −1,0,1,2, … } 3 ___ Integers D. {… , −2, − , 0,1.5, … } 2 ___ Whole Numbers E. {… , −√5, √2, �, … } 3 ___ Natural Numbers F. {… , − , 0,4, �, … } 2 Describe what the diagram above tells us about the relationship between natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ - I can define natural numbers and list the number set. - I can define whole numbers and list the number set. - I can define integers and list the number set. - I can define rational numbers and explain why a given number is rational. - I can define irrational numbers and explain why a given number is irrational. - I can define real numbers and explain why a given number is real. - I can create the “Numbers Web” and explain how each number set is related. Natural Numbers (denoted , ℕ ): { 1, 2, 3, 4, . } - Numbers we use for counting. - Set of all the positive integers. Whole Numbers (denoted �): {0, 1, 2, 3, 4, . } - Nonnegative numbers that can be written without a fraction or decimal. - Set of all the nonnegative integers. Integers (denoted ℤ): {. , −2, −1,0,1,2, . } - A number that can be written without a fractional part. 5 1 Rational Numbers (denoted ℚ): {… − 10, − , 0, , 0.6, √25, 19. 51 … } 6 3 � - All numbers that can be written as a fraction, , where � and � are integers and � ≠ 0. � - All numbers are either terminating or repeating. Irrational Numbers (denoted �): {...,0.56093271546 … , √2, �, 1.21211211121111,… } � - Numbers that CANNOT be written as a fraction, , when � and � are integers and � ≠ 0. � - All numbers that are non-terminating and non-repeating. 18 Real Numbers (denoted ℝ): … , −17.5102, − , 0, √15, �, 10, … 4 - All the rational and irrational numbers. 1) Match each set of numbers with their most appropriate classification. Classifications: Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Imaginary Numbers √2 5 a) √7, �, , −7.5� b) 0, 5, 10, 15 c) − , 12, 16.5, √100 5 2 _________________ __________________ ___________________ 9 � d) √−16,√−20, 72� e) −9, −1, 6, 29, 1076 f) −15.5, − , 0.001, , �, 97 5 2 _________________ __________________ ___________________ 2) What type of number is −7? 3) Which does not describe 107? a) whole number a) whole number b) irrational number b) integer c) integer c) real number d) imaginary number d) irrational number 4) Which would be the most appropriate domain for finding you weight in pounds? a) integers b) rational numbers c) positive integers d) positive rational numbers 5) Nancy was asked the question, “Is the number � a rational or irrational number?” She answered, “The 2 number � is a rational number because it can be represented as a fraction. Is Nancy correct? Explain 2 your reasoning. 6) Which statement is not always true? a) The sum of two rational numbers is rational. b) The product of two irrational number is rational. c) The sum of a rational number and an irrational number is irrational. d) The product of a nonzero rational number and an irrational number is irrational. - I can define natural numbers and list the number set. ____________________________________________________________________________________ ____________________________________________________________________________________ - I can define whole numbers and list the number set. ____________________________________________________________________________________ ____________________________________________________________________________________ - I can define integers and list the number set. ____________________________________________________________________________________ ____________________________________________________________________________________ - I can define rational numbers and explain why a given number is rational. Define the set of rational numbers. Then, explain why 5 is a rational number. 7 ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ - I can define irrational numbers and explain why a given number is irrational. Define the set of rational numbers. Then, explain why √2 is an irrational number. ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ - I can define real numbers and explain why a given number is real. Define the set of real numbers. Then explain why √19 is a real number. ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ - I can create the “Numbers Web” and explain how each number set is related. ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ Name: ________________________ Date: ____________ Classwork/Homework: Classifying Numbers 1 What type of number is √17 ? 2 What type of number is 16.2? (1) rational number (3) imaginary number (1) rational number (3) integer (2) irrational number (4) whole number (2) irrational number (4) whole number 3 All of the following numbers are integers except 4 If � is whole number, then −7� must be a (1) −18 (3) 6.5 (1) whole number (3) irrational number (2) 0 (4) 1,500 (2) integer (4) imaginary number 5 Write a fraction that is not a rational number Explain why this fraction is not a rational number 6 The cost of production of shoes in a factory is most appropriately represented by (1) nonnegative rational numbers (3) nonnegative real numbers (2) integers (4) irrational numbers 7 Describe a scenario when it would be most appropriate to use rational numbers. 8 You are counting the number of dogs at a local dog park. What set of numbers would be most appropriate to use? 1 1 1 (1) {… − 2, −1,0,1,2, … } (3) {0, , 1, 1 , 2, 2 , 3, … } 2 2 2 (2) {0,1,2,3,4,5, … } (4) {−1,0,1,2,3,4} 9 Given the following expressions: 1 9 I. − + III. √16 ∙ � 2 2 14� II. IV. 7(√81) � Which expression(s) result in an integer? (1) I,II,IIV (3) I,III,IV (2) I,IV, only (4) II, only 10 Which statement is not always true? (1) The product of an integer and a whole number is an integer. (2) The product of an integer and a whole number is a whole number. (3) The sum of two rational numbers is rational. (4) The difference of two real numbers is real. 11 Could you ever add a rational number and an irrational number to obtain a rational number? If yes, provide an example. If no, explain your reasoning. 12 Determine if the sum of 5√7 and 2√7 is rational or irrational. Explain your answer. 13 14 15 Could you ever multiply an irrational number by an irrational number to obtain a rational number? If yes, provide an example. If no, explain your reasoning. 16 Given the following expressions: 1 9 17 13 I. − + III. − √ 2 2 4 4 II. 4� − 1 IV. (√10)(√10) Which expression(s) result in an irrational number? (1) II, only (3) I, II, III, IV (2) IV, only (4) II, III 17 Which statement is not always true? (Select all that apply) (1) The product two irrational numbers is irrational. (2) The product of two rational numbers is rational. (3) The sum of two irrational numbers is irrational. (4) The difference of a rational number and an irrational number is irrational. 18 Match each set of numbers with their most appropriate classification. Classifications: Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Imaginary Numbers a) {… , −2, −1,0,1,2, … } b) {0,1,2,3,4, … } c) −8�, √−5, √−49 _________________ __________________